A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a nontrivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. Additionally, the method is tested on a complex chance constrained unmanned aerial vehicle problem. The results show that this new method can be used to reliably solve chance constrained optimal control problems.

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用偏差核密度估计器解决机会约束最优控制问题的方法

开发了一种方法来数值求解机会约束最优控制问题。机会约束被重新表述为保留原始约束的概率属性的非线性约束。重构将机会约束的最优控制问题转换为可以数值求解的确定性最优控制问题。本文开发的新方法使用马尔可夫链蒙特卡洛采样和核密度估计器来近似机会约束，其核具有积分函数，该积分函数限制了指标函数。由应用内核密度估计器得到的非线性约束的设计边界不违反原始机会约束的边界。该方法在软着陆最佳控制问题的非平凡机会约束修改上进行了测试，并将结果与​​使用最佳控制问题的保守确定性公式获得的结果进行了比较。此外，该方法针对机会受限的无人机问题进行了测试。结果表明，该新方法可用于可靠地解决机会约束最优控制问题。